结果的标识日志Det=跟踪日志的模拟

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摘要翻译：
结果$R_{r_1,...,r_n}$定义了一个由$N$变量中的$r_1,...,r_n$次的齐次多项式组成的系统的可解性条件，就像行列式对线性方程组的可解性一样。正因为如此，结式是即将到来的非线性物理的重要特殊函数，并开始在与弦理论有关的各种主题中发挥作用。不幸的是，当变量数较大时，缺少方便的结果公式。为了解决这个问题，我们将著名的身份日志Det=Trace日志从行列式推广到结果式。广义恒等式允许得到多维结式的显式多项式公式：对于任意数目的变量，结式由Schur多项式给出。我们还给出了几种结果的积分表示，以及一种路径上的和表示。
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英文标题：
《Analogue of the identity Log Det = Trace Log for resultants》
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作者：
A.Morozov and Sh.Shakirov
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最新提交年份：
2008
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分类信息：

一级分类：Physics        物理学
二级分类：Mathematical Physics        数学物理
分类描述：Articles in this category focus on areas of research that illustrate the application of mathematics to problems in physics, develop mathematical methods for such applications, or provide mathematically rigorous formulations of existing physical theories. Submissions to math-ph should be of interest to both physically oriented mathematicians and mathematically oriented physicists; submissions which are primarily of interest to theoretical physicists or to mathematicians should probably be directed to the respective physics/math categories
这一类别的文章集中在说明数学在物理问题中的应用的研究领域，为这类应用开发数学方法，或提供现有物理理论的数学严格公式。提交的数学-PH应该对物理方向的数学家和数学方向的物理学家都感兴趣；主要对理论物理学家或数学家感兴趣的投稿可能应该指向各自的物理/数学类别
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一级分类：Physics        物理学
二级分类：High Energy Physics - Theory        高能物理-理论
分类描述：Formal aspects of quantum field theory. String theory, supersymmetry and supergravity.
量子场论的形式方面。弦理论，超对称性和超引力。
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一级分类：Mathematics        数学
二级分类：Algebraic Geometry        代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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一级分类：Mathematics        数学
二级分类：Mathematical Physics        数学物理
分类描述：math.MP is an alias for math-ph. Articles in this category focus on areas of research that illustrate the application of mathematics to problems in physics, develop mathematical methods for such applications, or provide mathematically rigorous formulations of existing physical theories. Submissions to math-ph should be of interest to both physically oriented mathematicians and mathematically oriented physicists; submissions which are primarily of interest to theoretical physicists or to mathematicians should probably be directed to the respective physics/math categories
math.mp是math-ph的别名。这一类别的文章集中在说明数学在物理问题中的应用的研究领域，为这类应用开发数学方法，或提供现有物理理论的数学严格公式。提交的数学-PH应该对物理方向的数学家和数学方向的物理学家都感兴趣；主要对理论物理学家或数学家感兴趣的投稿可能应该指向各自的物理/数学类别
--

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英文摘要：
  Resultant $R_{r_1, ..., r_n}$ defines a condition of solvability for a system of $n$ homogeneous polynomials of degrees $r_1, ..., r_n$ in $n$ variables, just in the same way as determinant does for a system of linear equations. Because of this, resultants are important special functions of upcoming non-linear physics and begin to play a role in various topics related to string theory. Unfortunately, there is a lack of convenient formulas for resultants when the number of variables is large. To cure this problem, we generalize the well-known identity Log Det = Trace Log from determinants to resultants. The generalized identity allows to obtain explicit polynomial formulas for multidimensional resultants: for any number of variables, resultant is given by a Schur polynomial. We also give several integral representations for resultants, as well as a sum-over-paths representation.
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PDF链接：
https://arxiv.org/pdf/0804.4632

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关键词：Mathematical formulations Applications Presentation Determinants 日志 well 得到 linear 恒等式